Derivation and Verification of Intrinsic Dynamics in Financial Trading: Necessary Laws Forced by Settlement Conservation

Abstract:This paper establishes an axiomatic foundation for financial trading dynamics, moving beyond traditional statistical fitting to derive strict intrinsic laws from settlement conservation. By formalizing market mechanics through four fundamental elements—structural constraints (Red Line), forbidden states (Red Zone), legitimate operational paths (Green Line), and stable operational intervals (Green Zone)—we construct a rigorous mathematical framework comprising axioms (A0–A3), root theorems, and spectral bounds. Empirical validation across high-frequency datasets of 300 stocks demonstrates that the system achieves machine-precision convergence (10^-16) under constrained projections and robustly preserves conservation structures within a 10^-5 relative scale under unconstrained estimation. Note on Version:This is the finalized v6.95 manuscript, featuring complete axiom chains, rigorous spectral proofs, dual-layer numerical verification certificates, and comprehensive appendices.